#pragma once

// Standard C++ library includes
#include <cassert>
#include <cmath>
#include <limits>

#ifndef ABS
	#define ABS(x) ((x)<0?-(x):(x))
#endif

// Sort out the missing round function in MSVC:
#if defined( WIN32 ) && defined( _MSC_VER )
	inline double round(const double x) 
	{
		return x < 0.0 ? ceil(x - 0.5) : floor(x + 0.5);
	}
#endif

static const float FLT_STD_EPSILON = std::numeric_limits<float>::epsilon();
static const float FLT_STD_MAX = std::numeric_limits<float>::max();
static const float FLT_ZERO_TOLERANCE = 1e-06f;
static const float FLT_PI = 4.0f*std::atan(1.0f);
static const float FLT_TWO_PI = 2.0f*FLT_PI;
static const float FLT_HALF_PI = 0.5f*FLT_PI;
static const float FLT_INVERSE_PI = 1.0f/FLT_PI;
static const float FLT_INVERSE_TWO_PI = 1.0f/FLT_TWO_PI;
static const float FLT_DEG_TO_RAD = FLT_PI/180.0f;
static const float FLT_RAD_TO_DEG = 180.0f/FLT_PI;
static const float FLT_LOG_2 = std::log(2.0f);
static const float FLT_LOG_10 = std::log(10.0f);
static const float FLT_INV_LOG_2 = 1.0f/std::log(2.0f);
static const float FLT_INV_LOG_10 = 1.0f/std::log(10.0f);

static const double DBL_STD_EPSILON = std::numeric_limits<double>::epsilon();
static const double DBL_STD_MAX = std::numeric_limits<double>::max();
static const double DBL_ZERO_TOLERANCE = 1e-08;
static const double DBL_PI = 4.0*std::atan(1.0);
static const double DBL_TWO_PI = 2.0*DBL_PI;
static const double DBL_HALF_PI = 0.5*DBL_PI;
static const double DBL_INVERSE_PI = 1.0/DBL_PI;
static const double DBL_INVERSE_TWO_PI = 1.0/DBL_TWO_PI;
static const double DBL_DEG_TO_RAD = DBL_PI/180.0;
static const double DBL_RAD_TO_DEG = 180.0f/DBL_PI;
static const double DBL_LOG_2 = std::log(2.0);
static const double DBL_LOG_10 = std::log(10.0);
static const double DBL_INV_LOG_2 = 1.0/std::log(2.0);
static const double DBL_INV_LOG_10 = 1.0/std::log(10.0);

template <class numT>
struct float_traits { };

template <>
struct float_traits<float> 
{
	typedef float float_type;
	static inline float_type epsilon() { return FLT_STD_EPSILON; }
	static inline float_type zeroTolerance() { return FLT_ZERO_TOLERANCE; }
	static inline float_type max() { return FLT_STD_MAX; }
	static inline float_type pi() { return FLT_PI; }
	static inline float_type twoPi() { return FLT_TWO_PI; }
	static inline float_type halfPi() { return FLT_HALF_PI; }
	static inline float_type inversePi() { return FLT_INVERSE_PI; }
	static inline float_type inverseTwoPi() { return FLT_INVERSE_TWO_PI; }
	static inline float_type degToRad() { return FLT_DEG_TO_RAD; }
	static inline float_type radToDeg() { return FLT_RAD_TO_DEG; }
	static inline float_type log2() { return FLT_LOG_2; }
	static inline float_type log10() { return FLT_LOG_10; }
	static inline float_type invLog2() { return FLT_INV_LOG_2; }
	static inline float_type invLog10() { return FLT_INV_LOG_10; }
};

template <>
struct float_traits<double> 
{
	typedef double float_type;
	static inline float_type epsilon() { return DBL_STD_EPSILON; }
	static inline float_type zeroTolerance() { return DBL_ZERO_TOLERANCE; }
	static inline float_type max() { return DBL_STD_MAX; }
	static inline float_type pi() { return DBL_PI; }
	static inline float_type twoPi() { return DBL_TWO_PI; }
	static inline float_type halfPi() { return DBL_HALF_PI; }
	static inline float_type inversePi() { return DBL_INVERSE_PI; }
	static inline float_type inverseTwoPi() { return DBL_INVERSE_TWO_PI; }
	static inline float_type degToRad() { return DBL_DEG_TO_RAD; }
	static inline float_type radToDeg() { return DBL_RAD_TO_DEG; }
	static inline float_type log2() { return DBL_LOG_2; }
	static inline float_type log10() { return DBL_LOG_10; }
	static inline float_type invLog2() { return DBL_INV_LOG_2; }
	static inline float_type invLog10() { return DBL_INV_LOG_10; }
};

template <typename T>
class Math 
{
public:
	typedef T num_type;
	typedef float_traits<num_type> traits_type;

	static inline num_type epsilon() { return traits_type::epsilon(); }
	static inline num_type zeroTolerance() { return traits_type::zeroTolerance(); }
	static inline num_type max() { return traits_type::max(); }
	static inline num_type pi() { return traits_type::pi(); }
	static inline num_type twoPi() { return traits_type::twoPi(); }
	static inline num_type halfPi() { return traits_type::halfPi(); }
	static inline num_type inversePi() { return traits_type::inversePi(); }
	static inline num_type inverseTwoPi() { return traits_type::inverseTwoPi(); }
	static inline num_type degToRad() { return traits_type::degToRad(); }
	static inline num_type radToDeg() { return traits_type::radToDeg(); }
	static inline num_type log2() { return traits_type::log2(); }
	static inline num_type log10() { return traits_type::log10(); }
	static inline num_type invLog2() { return traits_type::invLog2(); }
	static inline num_type invLog10() { return traits_type::invLog10(); }

	static T ACos(T _val);
	static T ASin(T _val);
	static T ATan(T _val);
	static T ATan2(T _x, T _y);
	static T Ceil(T _val);
	static T Cos(T _val);
	static T Exp(T _val);
	static T FAbs(T _val);
	static T Floor(T _val);
	static T FMod (T _x, T _y);
	static T InvSqrt(T _val);
	static T Log(T _val);
	static T Log2(T _val);
	static T Log10(T _val);
	static T Pow(T _base, T _exponent);
	static T Sin(T _val);
	static T Sqr(T _val);
	static T Sqrt(T _val);
	static T Tan(T _val);
};

typedef Math<float> Mathf;
typedef Math<double> Mathd;

template<typename T>
inline T Math<T>::ACos(T _val) 
{
	if (-static_cast<T>(1) < _val) 
	{
		if (_val < static_cast<T>(1)) 
		{
			return static_cast<T>(std::acos(_val));
		}
		else 
		{
			return static_cast<T>(0);
		}
	}
	else 
	{
		return pi();
	}
}

template <class T>
inline T Math<T>::ASin(T _val) 
{
	if (-static_cast<T>(1) < _val) 
	{
		if (_val < static_cast<T>(1)) 
		{
			return static_cast<T>(std::asin(_val));
		}
		else 
		{
			return halfPi();
		}
	}
	else 
	{
		return -halfPi();
	}
}

template <class T>
inline T Math<T>::ATan(T _val) 
{
	return static_cast<T>(std::atan(_val));
}

template <class T>
inline T Math<T>::ATan2(T _x, T _y) 
{
	return static_cast<T>(std::atan2(_x, _y));
}

template <class T>
inline T Math<T>::Ceil(T _val) 
{
	return static_cast<T>(std::ceil(_val));
}

template <class T>
inline T Math<T>::Cos(T _val) 
{
	return static_cast<T>(std::cos(_val));
}

template <class T>
inline T Math<T>::Exp(T _val)
{
	return static_cast<T>(std::exp(_val));
}

template <class T>
inline T Math<T>::FAbs(T _val) 
{
	return static_cast<T>(std::fabs(_val));
}

template <class T>
inline T Math<T>::Floor(T _val) 
{
	return static_cast<T>(std::floor(_val));
}

template <class T>
inline T Math<T>::FMod(T _x, T _y) 
{
	return static_cast<T>(std::fmod(_x, _y));
}

template <class T>
inline T Math<T>::InvSqrt(T _val) 
{
	return static_cast<T>(1/std::sqrt(_val));
}

template <class T>
inline T Math<T>::Log(T _val) 
{
	return static_cast<T>(std::log(_val));
}

template <class T>
inline T Math<T>::Log2(T _val) 
{
	return invLog2() * static_cast<T>(std::log(_val));
}

template <class T>
inline T Math<T>::Log10(T _val) 
{
	return invLog10() * static_cast<T>(std::log(_val));
}

template <class T>
inline T Math<T>::Pow(T _base, T _exponent) 
{
	return static_cast<T>(std::pow(_base, _exponent));
}

template <class T>
inline T Math<T>::Sin(T _val) 
{
	return static_cast<T>(std::sin(_val));
}

template <class T>
inline T Math<T>::Sqr(T _val) 
{
	return _val*_val;
}

template <class T>
inline T Math<T>::Sqrt(T _val) 
{
	return static_cast<T>(std::sqrt(_val));
}

template <class T>
inline T Math<T>::Tan(T _val) 
{
	return static_cast<T>(std::tan(_val));
}

/** Returns the next higher power of 2 based on the passed argument
 */
inline unsigned nextPow2(unsigned x)
{
	--x;
	x |= x >> 1;
	x |= x >> 2;
	x |= x >> 4;
	x |= x >> 8;
	x |= x >> 16;
	return ++x;
}
